Is it permissible for the atheist father or brothers of a committed Muslim girl to be her guardians (wali) in court to solemnize her marriage? And what is the solution for that?

For a marriage (nikah) to be Islamically valid, a guardian (wali) and two witnesses are required. The guardian must be Muslim if the girl is Muslim. If there is no Muslim guardian or Muslim ruler, the girl may appoint a righteous Muslim man to act as her guardian for the marriage contract. If the girl's family are atheists, the Muslim ruler or his deputy (such as the head of the Sharia court) undertakes her marriage contract. If neither is available, she may appoint a righteous Muslim man to marry her, after verifying the absence of a Muslim guardian.